The best way to really appreciate the depth of the canyon is the relatively short Santa Elena Canyon Trail, which follows the Rio Grande for a short distant into the gorge. A very shot, steep section near the start and can be tricky crossing Terlingua Creek - otherwise an easy and flat walk.
Track notes and photos: https://hikingtheworld.blog/2017/10/28/the-best-of-big-bend-texas/#Santa-Elena-Canyon